13 percent to 23 percent, according to documents viewed by Reuters. When plans covering families are included, rates rise anywhere from 8 to 36 percent.

Wal-Mart does offer some plans with premiums that are well below the national average. Wal-Mart's lowest-cost and most popular associate-only medical plan will cost $17.40 per two-week pay period in 2013, up $2 from 2012. Costs for a single non-tobacco-using employee range from that to $59.30 per paycheck for 2013 (or $34.80 to $118.60 every four weeks).

According to the Kaiser Family Foundation's 2012 survey, the average monthly U.S. worker contribution this year was $79 per month for single coverage.

U.S. premiums are expected to rise 6.3 percent on average in 2013, human resources firm Aon Hewitt said in October, but premiums are just part of the costs story.

Newly hired part-time employees at Wal-Mart will have to work a minimum of 30 hours a week, up from 24 hours previously, before they qualify for coverage. The Affordable Care Act only requires larger employers to provide coverage for their staff who work at least 30 hours per week.

Other changes to Wal-Mart's 2013 plans, such as raising premiums, would have happened regardless of Obamacare, as it tries to control rising healthcare costs, the company said.

Harris and Andridge, who are dropping their coverage, are part of a group called OUR Walmart. Higher healthcare costs are one of the issues the group wants Wal-Mart to address, along with concerns such as wages and scheduling.

Even if the plan only went up, let's say 50 cents, when you're barely making it every literal cent counts, said Harris.

OUR Walmart, which itself is not a labor union, is backed by the United Food and Commercial Workers International union, which represents workers at major grocery chains that compete with Wal-Mart. Members of OUR Walmart pay the organization dues of $5 per month.